A hybrid approach for the regularized long wave-Burgers equation

Asuman Zeytinoglu, Murat Sari, Bilender P. Allahverdiev

Abstract

In this paper, a new hybrid approach based on sixth-order finite difference and seventh-order weighted essentially non-oscillatory finite difference scheme is proposed to capture numerical simulation of the regularized long wave-Burgers equation which represents a balance relation among dissipation, dispersion and nonlinearity. The corresponding approach is implemented to the spatial derivatives and then MacCormack method is used for the resulting system. Some test problems discussed by different researchers are considered to apply the suggested method. The produced results are compared with some earlier studies, and to validate the accuracy and efficiency of the method, some error norms are computed. The obtained solutions are in good agreement with the literature. Furthermore, the accuracy of the method is higher than some previous works when some error norms are taken into consideration.

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References

Bona, J.L., Pritchard, W.G. & Scott, L.R. (1981). An evaluation of a model equation for water waves. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 302(1471), 457-510.